Question

in scalar product, prove that A.A=1 ...​

Answer 1

Explanation:

Scalar product of two vector quantities is defined as

X. Y

and it has the form

$x.y = |x | |y| \ \cos( \alpha )$

Here alpha is the angle between the two vector quantities

Now if both the vectors are same they will point in same direction. So the angle between them( alpha) will be zero

So let the vectors be A

$a.a = |a| |a| \cos(0)$

$a.a = | {a}^{2} |$

since cos( 0)=1

And if the magnitude of A is one (i.e it is a unit vector)

$a.a = {1}^{2}$

i. e

$a.a = 1$

Hence proved